Séminaire Lotharingien de Combinatoire, 95B.96 (2026), 12 pp.
Guilherme Zeus Dantas e Moura and Olya Mandelshtam
Shape Changing Identities for Permuted-Basement Nonsymmetric Macdonald Polynomials
Abstract.
Permuted-basement Macdonald
polynomials Eασ(x;q,t)
are nonsymmetric generalizations of symmetric Macdonald polynomials
that form a basis for the polynomial
ring Q(q,t)[x] for each fixed
σ. There are combinatorial formulas for them as generating
functions over composition-shaped non-attacking fillings. In this
extended abstract, we bijectively prove identities for the
relationship between Eασ,
Eασsi,
Esiασ,
and Esiασsi. These
identities correspond to two combinatorial operations on non-attacking
fillings: (1) swapping adjacent entries in the basement,
generalizing a result of Alexandersson (2019), and (2) swapping
adjacent parts in the shape, which yields a straightening rule
for expanding
Eασ in the polynomials
{Esiατ}τ.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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